AnswersAlgebra IIGraphs of Rational Functions

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At which values of x does the graph of f of x is equal to the fraction with numerator x squared minus x minus 2 and denominator open paren x squared minus 1 close paren times open paren x squared minus 16 close paren have a vertical asymptote? Choose three correct answers.

A
negative 1
B
1
C
4
D
2
E
negative 4
2
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Which statements describe the key features of the graph of f of x is equal to the fraction with numerator 18 minus 3 x minus x squared and denominator x squared minus 9 ? Choose three correct answers.

A
The graph has an x -intercept at negative 6 .
B
The graph has a vertical asymptote at x is equal to 3 .
C
The graph has a y -intercept at negative 2 .
D
The graph has a vertical asymptote at x is equal to negative 3 .
E
The graph has a horizontal asymptote at y is equal to 1 .
3

The graph of f of x is equal to the fraction with numerator 24 x squared plus 62 x plus 34 and denominator 4 x plus 3 has an oblique asymptote at y is equal to

A
x plus 1 .
B
4 x plus 3 .
C
62 x plus 34 .
D
6 x plus 11 .
4

f of x is equal to the fraction with numerator open paren x minus 2 close paren times open paren x plus 1 close paren and denominator x plus 1 Which statements describe the end behavior of the graph of the function shown? Choose two correct answers.

A
As x rightarrow infinity , y rightarrow infinity .
B
As x rightarrow negative infinity , y rightarrow infinity .
C
As x rightarrow infinity , y rightarrow 1 .
D
As x rightarrow negative infinity , y rightarrow negative infinity .
E
As x rightarrow infinity , y rightarrow negative infinity .
F
As x rightarrow negative infinity , y rightarrow 1 .
5

Which function has a graph with a horizontal asymptote at y is equal to 3 , a vertical asymptote at x is equal to 1 , and an x -intercept at 2 ?

A
f of x is equal to the fraction with numerator 3 times open paren x minus 1 close paren and denominator x minus 2
B
f of x is equal to the fraction with numerator x minus 1 and denominator 3 times open paren x minus 2 close paren
C
f of x is equal to the fraction with numerator 3 times open paren x minus 2 close paren and denominator x minus 1
D
f of x is equal to the fraction with numerator x minus 2 and denominator 3 times open paren x minus 1 close paren
9

f of x is equal to the fraction with numerator x squared plus x plus 1 and denominator 6 times open paren x minus 4 close paren g of x is equal to the fraction with numerator x squared plus x plus 1 and denominator 8 times open paren x minus 4 close paren Which statement comparing the oblique asymptotes of the functions f of x and g of x is true?

A
The oblique asymptote for g of x is steeper than for f of x .
B
The oblique asymptote for f of x is steeper than for g of x .
C
Both functions have the same oblique asymptote.
D
Both functions have parallel oblique asymptotes.

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